Carrier track loop for GNSS Derived attitude

ABSTRACT

A method and system for reducing Global Navigation Satellite System (GNSS) carrier tracking loop ambiguities comprising: receiving a plurality of GNSS satellite signals with a first antenna in operable communication with a first tracking device and a second antenna in communication with a second tracking device in at least one GNSS receiver; and sharing of data between the first tracking device and the second tracking device. The sharing is configured to facilitate a commonality in a carrier phase derived in the first and second tracking devices. The sharing also results in a cancellation of the commonality when a difference phase is formed between a carrier phase from the first tracking device and a carrier phase from the second tracking device.

FIELD OF THE INVENTION

The invention relates generally to precision GNSS location or attitudesystems. More specifically, the invention relates to systems thatutilize Global Navigation Satellite System (GNSS) signals to inferdifferential path length of carrier signals arriving at two or moreantennas.

BACKGROUND OF THE INVENTION

The determination of the orientation of an object's axes relative to areference system is often of interest. Depending on the application, theorientation and reference system may be in two dimensions (2D) or inthree dimensions (3D). In the case of two-dimensional systems, termssuch as azimuth, heading, elevation, pitch, and inclination may be usedin place of attitude.

There are many techniques in use to measure 2D and 3D attitude. Commontechniques include using a magnetic compass to reference the object ofinterest to the local gravitational field, optical techniques toreference the object of interest to an earth-based or star-basedreference frame, accelerometers to measure relative attitude or changesin attitude, and optical and mechanical gyroscopes for also measuringrelative attitude. The merits of each technique are best judgedaccording to the specific application or use. Likewise, each techniquealso exhibits disadvantages that may include accuracy, cost, and ease ofuse.

Recently, attitude determination using highly accurate space-based radionavigation systems has become possible. Such a radio navigation systemis commonly referred to as a Global Navigation Satellite System (GNSS).A GNSS includes a network of satellites that broadcast radio signals,enabling a user to determine the location of a receiving antenna with ahigh degree of accuracy. To determine the attitude of an object, it issimply necessary to determine the position of two or more receivingantennas that have known placements relative to an object. Examples ofGNSS systems include Navstar Global Positioning System (GPS),established by the United States; Globalnaya Navigatsionnay SputnikovayaSistema, or Global Orbiting Navigation Satellite System (GLONASS),established by the Russian Federation and similar in concept to GPS; andGalileo, also similar to GPS but created by the European Community andslated for full operational capacity in 2008.

Should it be necessary to improve the accuracy, reliability, orconfidence level of an attitude or position determined through use of aGNSS, a Satellite-Based Augmentation System (SBAS) may be incorporatedif one that is suitable is available. There are several public SBAS thatwork with GPS. These include Wide Area Augmentation System (WAAS),developed by the United States' Federal Aviation Authority, EuropeanGeostationary Navigation Overlay Service (EGNOS), developed by theEuropean Community, as well as other public and private pay-for-servicesystems.

Currently the best-known of the available GNSS, GPS was developed by theUnited States government and has a constellation of 24 satellites in 6orbital planes at an altitude of approximately 26,500 km. The firstsatellite was launched in February 1978. Initial Operational Capability(IOC) for the GPS was declared in December 1993. Each satellitecontinuously transmits microwave L-band radio signals in two frequencybands, L1 (1575.42 MHz) and L2 (1227.6 MHz). The L1 and L2 signals arephase shifted, or modulated, by one or more binary codes. These binarycodes provide timing patterns relative to the satellite's onboardprecision clock (synchronized to other satellites and to a groundreference through a ground-based control segment), in addition to anavigation message giving the precise orbital position of eachsatellite, clock correction information, and other system parameters.

The binary codes providing the timing information are called the C/ACode, or coarse acquisition code, and the P-code, or precise code. TheC/A Code is a 1 MHz Pseudo Random Noise (PRN) code modulating the phaseof the L1 signal and repeating every 1023 bits (one millisecond). TheP-Code is also a PRN code, but modulates the phase of both the L1 and L2signals and is a 10 MHz code repeating every seven days. These PRN codesare known patterns that can be compared to internal versions in thereceiver. The GNSS receiver is able to compute an unambiguous range toeach satellite by determining the time-shift necessary to align theinternal code to the broadcast code. Since both the C/A Code and theP-Code have a relatively long “wavelength”—approximately 300 meters (or1 microsecond) for the C/A Code and 30 meters (or 1/10 microsecond) forthe P-Code, positions computed using them have a relatively coarse levelof resolution.

To improve the positional accuracy provided by use of the C/A Code andthe P-Code, a receiver may take advantage of the carrier component ofthe L1 or L2 signal. The term “carrier”, as used herein, refers to thedominant spectral component remaining in the radio signal after thespectral content resulting from the modulating PRN digital codes hasbeen removed (e.g., from the C/A Code and the P-Code). The L1 and L2carrier signals have wavelengths of about 19 centimeters and 24centimeters, respectively. The GPS receiver is able to track thesecarrier signals and measure the carrier phase to a small fraction of acomplete wavelength, permitting range measurement to an accuracy of lessthan a centimeter.

A technique to improve accuracy is realized by differencing GPS rangemeasurements—known as Differential GPS (DGPS). The combination of DGPSwith precise measurements of carrier phase leads to differentialposition accuracies of less than one centimeter root-mean-squared (i.e.,centimeter-level positioning). Such accuracies are sufficient todetermine the attitude of an object with 2 or more GPS GNSS antennas,typically spaced from 0.2 meters to 2 meters apart.

Accurate differential carrier phase is a primary concern for attitudedetermination or other precise GNSS positioning. Carrier phase data isavailable by tracking the carrier phase on either the L1 or L2 GPSsignal. Navigation data is BPSK modulated onto both the L1 and the L2carrier at a 50 Hz rate and, as such, the input carrier phase is subjectto a 180 degree phase reversal every 20 milliseconds and the absolutephase can be inverted. The data modulation is removed from the carrierby means of a tracking loop known as a Costas loop.

A Costas loop results in a 180 degree phase ambiguity. That is, theCostas loop is just as likely to phase lock so that the binary 1's comeout as binary 0's, and vice versa. The 180 degree phase ambiguity is ofconcern since it introduces an ambiguity of ½ of a carrier wavelength inthe measured carrier phase. The wavelength of the L1 carrier is about 19cm and the ½ cycle ambiguity is thus equivalent to 9.5 cm of measuredphase.

Typically, in GPS receivers, the ½ cycle ambiguity is resolved bylooking at certain data bits within the navigation message that are of aknown value. If the bit is inverted over its known value, then theCostas loop is locked to the opposite phase and ½ cycle's worth of phasemust be added to (or subtracted from) the measured carrier phase inorder to maintain whole cycle phase alignment. It is of littleconsequence whether the ½ cycle is added or subtracted from the measuredphase since, regardless, a whole cycle ambiguity is still present thatmust be removed by methods such as those described in U.S. Pat. No.6,469,663 and/or U.S. patent application Ser. No. 11/______, entitledAttitude Determination Exploiting Geometry Constraints, to Whitehead etal., Attorney Docket No. 100564.00023, filed Oct. 4, 2005.

One problem that arises is that known data bits, such as those in thenavigation message's preamble, arrive only so often. For example, thepreamble itself is sent once every six seconds as the start of a 300 bitlong sub-frame (see ICD-GPS-200). Other bits within the navigationmessage are known, or can be inferred from past data, but there arestill many bits which are not known or which may not be predicted with100% confidence. If the Costas loop is stressed (due to multipathfading, foliage attenuation, signal blockage, and the like) while theunknown bits are arriving, it may undergo a 180 degree phase shift thatis not immediately detected. Hence, a ½ cycle error will arise in themeasured phase that will persist until the next known data bit arrives.This may then reduce the accuracy in heading, pitch, or roll if themeasured phase is used in an attitude determining device.

A further complication of a Costas loop is that the probability for acycle slip is significantly higher when using a Costas loop as opposedto a conventional Phase Lock Loop (PLL). This is because the Costas loopis mathematically equivalent to a squaring loop that tracks the carrierphase at twice the carrier frequency. Phase tracking errors greater than90 degrees may cause cycle slips in a Costas loop whereas phase errorsof up to 180 degrees may be tolerated when using a PLL.

In an attitude system, such as that disclosed in Whitehead et al., thecarrier phases arriving at two or more separate antennas are differencedwith one another to create a differential carrier phase. The process oftaking the difference cancels common mode errors such as satellite clockerror and errors caused by propagation delays as the GNSS signal travelsthrough the ionosphere and troposphere.

What is needed then is a Costas loop method that results in common ½cycle ambiguity for carrier phases measured at both a master antenna andone or more slave antennas for a particular satellite. Being common, the½ cycle ambiguity will cancel in the differential carrier phase.

Secondly, what is also needed is a method to make up for the loss ofperformance of a Costas loop over a conventional PLL. Again, sincedifferencing is deployed, it is desirable that any cycle slips thatarise on a carrier signal tracked from one antenna be present in thecarrier signal tracked by a different antenna. Such cycle slips willcancel in the difference and will not affect the attitude or heading.

Thirdly, a method is needed that yields common, noise-induced effects ineach individually tracked carrier phase so that the common-mode effectscancel in the differential carrier phase. A method with theaforementioned properties is applied to carrier tracking loops receivingdata at two or more antennas that experience roughly similar motion ormotion for which relative dynamic effects are low. The method furtherhas the ability to track rapid clock-induced carrier phase when a commonclock is employed.

SUMMARY OF THE INVENTION

Disclosed herein in an exemplary embodiment is a method of reducingGlobal Navigation Satellite System (GNSS) carrier tracking loopambiguities comprising: receiving a plurality of GNSS satellite signalswith a first antenna in operable communication with a first trackingdevice and a second antenna in communication with a second trackingdevice in at least one GNSS receiver; and sharing of data between thefirst tracking device and the second tracking device. The sharing isconfigured to facilitate a commonality in a carrier phase derived in thefirst and second tracking devices. The sharing also results in acancellation of the commonality when a difference phase is formedbetween a carrier phase from the first tracking device and a carrierphase from the second tracking device.

Also disclosed herein in yet another exemplary embodiment is a systemfor reducing Global Navigation Satellite System (GNSS) carrier trackingloop ambiguities comprising: a first antenna in operable communicationwith a first tracking device configured to receive a plurality of GNSSsatellite signals; and a second antenna in communication with a secondtracking device configured to receive a plurality of GNSS satellitesignals. The first tracking device and the second tracking deviceoperable in at least one GNSS receiver. The first tracking device andthe second tracking device are configured to share data therebetween tofacilitate a commonality in a carrier phase derived in the firsttracking device and the second tracking device. A difference phase isformed between a carrier phase from the first tracking device andanother carrier phase from the second tracking device resulting in acancellation of the commonality.

Further disclosed herein in another exemplary embodiment is a system forreducing Global Navigation Satellite System (GNSS) carrier tracking loopambiguities comprising: means for receiving a plurality of GNSSsatellite signals with a first antenna in operable communication with afirst tracking device and a second antenna in communication with asecond tracking device in at least one GNSS receiver. The system alsoincludes means for sharing of data between the first tracking device andthe second tracking device, the sharing configured to facilitate acommonality in a carrier phase derived in the first tracking device andthe second tracking device. The sharing resulting in a cancellation inthe commonality when a difference phase is formed between a carrierphase from the first tracking device and another carrier phase from thesecond tracking device.

Disclosed herein in yet another exemplary embodiment is a storage mediumencoded with a machine-readable computer program code, the storagemedium including instructions for causing a computing system toimplement the abovementioned method for reducing Global NavigationSatellite System (GNSS) carrier tracking loop ambiguities.

Further, disclosed herein in yet another exemplary embodiment is acomputer data signal, the computer data signal comprising codeconfigured to cause a processor to implement the abovementioned methodfor reducing Global Navigation Satellite System (GNSS) carrier trackingloop ambiguities.

The invention also features a method for attitude determination or otherdifferential GNSS positioning applications that is effective at reducingthe occurrence of ½ ambiguities and cycle slips in the differentialcarrier phase. In an exemplary embodiment, this is accomplished bysharing information in the Costas tracking loops, designating onetracking device as a master while other slave tracking devices aredriven by a carrier discriminator employing the master's in-phase inplace of the slave's own in-phase data as is typically done. A relatedinvention yields the benefit of partially canceling common noise-inducedeffects in differential carrier phase measured between two antennas.

Additional features, functions, and advantages associated with thedisclosed methodology will be apparent from the detailed descriptionwhich follows, particularly when reviewed in conjunction with thefigures appended hereto.

BRIEF DESCRIPTION OF THE DRAWINGS

To assist those of ordinary skill in the art in making and using thedisclosed embodiments, reference is made to the appended figures,wherein like references are generally numbered alike in the severalfigures.

FIG. 1 is a diagram showing the use of GNSS satellites in an attitudedetermining system;

FIG. 2 is a schematic showing an attitude determining system embodimentof an exemplary embodiment of the present invention;

FIG. 3 is a block diagram of a carrier phase tracking and measuringsystem employing a Costas loop;

FIG. 4A shows true carrier phase error versus the in-phase signal;

FIG. 4B shows true carrier phase error versus the quadrature-phasesignal;

FIG. 4C shows a carrier discriminator for a Costas loop;

FIG. 4D shows a carrier discriminator for a conventional Phase LockLoop;

FIG. 5 is a block diagram of master and slave carrier phase track loopthat share the master's in-phase data in accordance with an exemplaryembodiment;

FIG. 6 is a block diagram showing multiple slave carrier phase trackerssharing data from a single master carrier phase tracker;

FIG. 7 is a block diagram depicts sharing of data between the Master andSlave carrier phase filters in accordance with an exemplary embodiment;and

FIG. 8 is a block diagram depicting sharing of data between the Masterand Slave carrier phase filters in accordance with another exemplaryembodiment.

DETAILED DESCRIPTION

An exemplary embodiment of invention features a method and system forattitude determination or other GNSS positioning that significantlyreduces the adverse effects of cycle slips and, simultaneously, problemsresulting from ½ cycle phase ambiguities, such as may be encounteredwhen employing a tracking loop, e.g., a phase tracking loop.

A preferred embodiment of the invention, by way of illustration, isdescribed herein as it may be applied to attitude determination. While apreferred embodiment is shown and described by illustration andreference to attitude determination, it will be appreciated by thoseskilled in the art that the invention is not limited to attitudedetermination alone and may be applied to control systems, navigation,and the like, as well as combinations thereof. An embodiment of theinvention as described herein may readily be applied to attitudedetermination as described in commonly assigned U.S. patent applicationSer. No. 11/______, entitled Attitude Determination Exploiting GeometryConstraints, Attorney Docket No. 100564.00023, filed Oct. 4, 2005, thecontents of which are incorporated by reference herein in theirentirety.

It will further be appreciated that, while particular sensors, antennas,receivers and the like nomenclature associated therewith are enumeratedto describe an exemplary embodiment, such terminology is utilized anddescribed for illustration only and are not limiting. Numerousvariations, substitutes, and equivalents will be apparent to thosecontemplating the disclosure herein.

FIG. 1 depicts an exemplary embodiment of an attitude determining system100 tracking a plurality of GNSS satellites, 101 through 103. Theattitude determining hardware system 100 includes the use of threeantennas to receive GNSS signals. Each satellite broadcasts a radiofrequency signal 104 that is picked up by two or more antennas, three ofwhich are shown as 105 through 107 in FIG. 1. The signal then travelsfrom each antenna into the receiver unit 108 where it is down-convertedand digitally sampled so that it may be tracked by the receiver'sdigital tracking loops. Various timing and navigation information isreadily extracted while tracking the signal, including the phase of aPseudo Random Noise (PRN) code timing pattern that is modulated on thesignal, the phase of the signal's carrier, and navigation data fromwhich the location of the satellite may be computed. It will beappreciated that while three antennas are depicted, more could beemployed if desired, especially for redundancy.

In order to perform the prescribed functions and desired processing, aswell as the computations therefor (e.g., the attitude determinationprocesses, and the like), the receiver 108 may include, but not belimited to, a processor(s), computer(s), memory, storage, register(s),timing, interrupt(s), communication interface(s), and input/outputsignal interfaces, and the like, as well as combinations comprising atleast one of the foregoing. For example, receiver 108 may include signalinterfaces to enable accurate down-conversion and digitally sampling andtracking of satellite signals as needed to facilitate extracting thevarious timing and navigation information, including, but not limitedto, the phase of the PRN code timing pattern. Additional features of thesystem 100, receiver 108 and the like, are thoroughly discussed herein.

One exemplary embodiment of an attitude determining system 100 shown inFIG. 2 uses a single receiver unit 201 containing multiple synchronizedtracking devices, 202 through 204, with each tracking device associatedwith exactly one antenna (205, 206, and 207). Each tracking device 202,203, and 204 is capable of tracking a plurality of satellites e.g., 101,102, and 103. Twelve or more satellites may be tracked. The trackingdevices 202, 203, and 204 serve the function of down converting thereceived Radio Frequency (RF) signals 104 arriving from the plurality ofsatellites e.g., 101, 102, and 103, sampling the composite signal, andperforming high-speed digital processing on the composite signal (suchas correlations with a PRN reference signal) that allow the code andcarrier phase of each satellite to be tracked. An example of suchsynchronized tracking devices 202, 203, and 204 is described in commonlyassigned U.S. patent application Ser. No. 11/029,809 entitled Method andSystem for Synchronizing Multiple Tracking Devices For A Geo-locationSystem, filed Jan. 5, 2005, which is a continuation-in-part of U.S.patent application Ser. No. 10/828,745 entitled Method And System ForSatellite Based Phase Measurements For Relative Positioning of Fixed OrSlow Moving Points in Close Proximity, filed Apr. 21, 2004, the contentsof which are incorporated by reference herein in their entirety. Eachtracking device, e.g., 202, 203, and 204 is connected to a single sharedcomputer processing unit (CPU) 208. The CPU 208 sends control commands210, 211, and 212 respectively to the plurality of tracking devices 202,203, and 204 that enable them to track the various GNSS satellites,e.g., 101, 102, and 103. The CPU 208 receives back from the trackingdevice code and carrier phase measurements of the various satellitesignals.

A synchronization signal 214, denoted as sync, sent by the mastertracking device 202 to the slave tracking devices 203 and 204 allows themaster tracking device 202 and slave tracking devices 203, 204 tomeasure the code and carrier phase of each satellite signal 104simultaneously. Furthermore, the RF down conversion within each trackingdevice 202, 203, and 204 and the sampling of data by each device is doneusing a common clock signal 220. When a single-difference phaseobservation is formed by subtracting the carrier (or code) phasemeasured by one tracking device with that measured by another trackingdevice for the same satellite, the portion of the phase due to thereceiver's clock error is essentially eliminated in the difference.

The use of a single CPU connected to multiple shared synchronizedtracking devices is advantageous. Data is easily shared among thetracking loops, and the carrier phase tracking loop may thus use amodified Costas loop. For any tracked satellite, e.g., 101, 102, 103,the in-phase reading from the Costas loop of a “master” tracking device,e.g., 202, dictates the sign of the quadrature-phase error discriminatornot only for itself, but also for the discriminator of Costas loops inthe remaining “slave” tracking devices, e.g., 203, 204. This forces thehalf-cycle phase ambiguity that is inherent in Costas tracking loops tobe the same across all tracking devices for any given satellite so thatit cancels when forming single-difference phase observations.Advantageously in this approach, the ambiguity is eliminated morequickly than methods that must wait to decode known navigation data bitsthat occur in headers or other parts of the navigation data.

FIG. 3 shows a Costas loop as may be employed for tracking the carriersignal in a GPS receiver in accordance with an exemplary embodiment. Tosimplify the figure and discussion, only the prompt channel isconsidered, as this is what is relevant to carrier tracking. The signalarrives at the antenna 401 and passes to the RF down conversion andsampling module 402. This results in an output of digitized IF sampledsignal denoted by reference numeral 403. The digitized IF signal 403 ismixed down to baseband by two multipliers 404 and 405 each driven by thenumerically controlled oscillator (NCO) 406. The NCO is an addressgenerator with sine/cosine lookup tables. The cosine signal 407 is keptin phase alignment with the carrier at its digitized IF. The sine signal408 is at 90 degrees phase offset (quadrature phase) relative to thecarrier at IF. Thus, the upper signal 409 is called the in-phase signaland the lower signal 410 is called the quadrature-phase signal.

In addition to driving the signals to baseband, the spreading PseudoRandom Noise (PN or PRN) sequence must be removed from the receivedsignal (e.g., CA code spreads the LI GPS signal). As depicted in thefigure, this is accomplished by multipliers 414 and 415 which multiplythe incoming signal by a replica model of the PN code that is generatedby the Code NCO and PN generator 416. In the case of carrier tracking(as opposed to code tracking), the replica model is called the prompt PNcode since it is steered by the code track-loop command 419 to align asclosely as possible to the actual PN spreading code on the receivedsignal (code tracking requires early and late combinations of a PN code,however this is not shown).

The data is then summed or low-pass filtered by summers 424 and 425,respectively. In the particular implementation shown, the summersperform sums over one millisecond which coincides with the length of theCA code's 1023 chip repetitive PN sequence (1023 chips with a 1.023 MHzchip rate yields a 1 millisecond span). Each summer accumulates anddumps its output. The in-phase output 426 is designated I_(P) ^(1ms) andthe quadrature phase output 427 is designated as Q_(p) ^(1ms) where thesuperscript ‘1 ms’ indicates that summation is over one millisecond andthe subscript ‘p’ indicates that this is the prompt channel (the channelrelevant to carrier phase tracking).

It is often advantageous, at least for the purpose of recovering thenavigation data bits, to increase the duration of the summations to span20 ms which is the length of one navigation data bit. There should be no180 degree phase shifts over the data bit's duration. Additional, butoptional, summers 434 and 435 serve the purpose of continuing the sumfor one data bit's duration and the Bit Synchronizer 436 controls thestart and stop of the summers 434, 435 to coincide with the bit edge.The result is an in-phase bit aligned signal 436 denoted as I_(p) ^(Bit)and is quadrature counter part Q_(p) ^(Bit) 437, respectively. Thein-phase component, I_(p) ^(Bit), is actually the demodulated navigationdata bit. It is noteworthy to appreciate that in practice, thisdemodulated navigation data bit I_(p) ^(Bit) Bit can take on a signopposite that of the true navigation data bit. However, the signreversal is readily corrected with the parity algorithm specified in theICD-GPS-200. The sign reversal, should it arise, is precisely aconsequence of using a Costas loop with its potential for ½ cycle phaseoffset. The sign reversal remains for all arriving demodulated data bitsuntil such a time that the track loop undergoes stress and slips back tothe true ½ cycle phase alignment.

Continuing with FIG. 3, the carrier discriminator block 450 serves thepurpose of producing a measure of the misalignment of the phase of thereference NCO signal 407 with the phase of the arriving carrier signalat the IF frequency. The measured phase error 451 is positive when thereference NCO phase is lagging the incoming carrier, negative when theNCO phase leads and zero otherwise. Furthermore, it has the propertythat its magnitude is roughly proportional to the magnitude of the truephase tracking error. A common Carrier Discriminator (CD) function isCD=Q _(p) sign(I _(p))where the sign( ) function takes the arithmetic sign (+1 or −1) of theenclosed argument which, in this case, is the sign of I_(p). Anothercommon discriminator function isCD=Tan⁻¹(Q _(p) /I _(p))

Many discriminator functions are known and may readily be found inliterature. Regardless of which is chosen, all serve the purpose ofacting as a measure of phase tracking error. When the discriminatorhovers around zero, the in-phase cosine signal 407 is properly alignedwith the incoming carrier.

In FIG. 3, in an exemplary embodiment, the carrier discriminator blockis shown to use the in-phase data 436 and quadrature phase data 437(I_(p) ^(Bit) and Q_(p) ^(Bit)) which are aligned to the navigation databits and summed over 20 milliseconds. It should be appreciated that thisapproach is just one possibility. It is also possible to supply thediscriminator with in-phase and quadrature-phase data has been summedover intervals of less then 20 milliseconds' duration. For example, theone millisecond summations I_(P) ^(1ms) and Q_(p) ^(1ms) may be usedinstead. It is for this purpose, that pickoff points 426 and 427 aredepicted. Once again, it should be appreciated that numerous otherpossibilities exist as well. Of course, it is advantageous that thesumming duration is selected as a multiple of one millisecond (the CAcode repetition rate) when tracking the L1 carrier using the CA code. Itis advantageous, in fact, to operate the track loop at a one millisecondupdate rate but run the in-phase summer from one to 20 millisecondstaking always the most recent sum for computing the carrierdiscriminator value each millisecond. The in-phase summer starts at thedata bit edge transition and continues summing to the end of the databit, in this instance, 20 milliseconds later. The in-phase sum, whenoperated in this manner, provides an increasingly better estimate of thesign of the data bit, thus slightly reducing the chance of ½ cycleslips.

To facilitate further discussion and simplify the notation, henceforth,the superscripts denoting the duration of summation (such as bit and 1ms) will be dropped with the understanding that a number of differentdurations are possible. The in-phase and quadrature phase data will bereferred to simply as I_(p) and Q_(p) hereafter.

Returning now to FIG. 3, the carrier tracking filter 452 takes the CDoutput denoted by reference numeral 451 as an input and produces an NCOstepping value 453 that is integrated (or summed) by the NCO 406 toproduce an NCO phase 460. The carrier tracking filter is often a Type 2filter, also known as a proportional-plus-integral (PI) filter orlead-lag filter, although other control schemes are certainly possible.The carrier tracking filter commands the carrier NCO 406 and eventuallyzeroes out the phase error at which point the CD output is essentiallyzero (or at least zero plus perhaps small tracking errors caused byrapid receiver or clock motion and noise effects).

The NCO's phase 460 is tapped off and sampled at a regular interval, sayfor example, every 1/20^(th) of a second. Since the NCO phase is alignedto the arriving carrier phase by the track loop, the NCO phase providesa measure of the arriving carrier phase. This measure, termed thecarrier phase observable, is used for carrier phase positioning, such asfor example, an attitude system that calculates heading, pitch, androll.

One thing that is evident, upon examination of the mathematicalequations governing the carrier discriminators, is that if both I_(p)and Q_(p) were to change sign, the discriminator output CD would remainunaffected since the change in sign cancels in the product (or quotient)of I_(p) and Q_(p). This is the desired effect of a Costas loop andresults in an immunity of the Costas loop to the sign of the navigationdata bit, which jointly effects the signs of both I_(p) and Q_(p).Otherwise, as for example if a simple PLL was used, every time thenavigation data bit changed sign, the loop would react in an undesirablefashion by attempting to track the instantaneous 180 degree phasereversals, and likely the loop would behave erratically.

However, the benefit of a Costas loop of the prior art is also itsdisadvantage when one desires to recover the phase of the carrierwithout introducing a ½ cycle ambiguity. Returning to FIG. 3, it shouldbe noted that a 180 degree shift in NCO phase will invert the sign ofboth the cosine term 407 and the sine term 408 ultimately resulting in asign reversal for both I_(p) and Q_(p). If the NCO undergoes a phaseshift of 180 degrees, the Costas loop, by itself, has no means torecognize the phase shift. When the Costas loop is stressed, perhaps bynoisy data or signal fades, it may erroneously shift the NCO phase by180 degrees at which point it may remain locked to the 180 degree shift.In the case of GPS, it is possible to eventually detect the occurrenceof a phase shift by monitoring the arriving data bits 436 and byrecognizing a discrepancy in the value of those bits whose value isknown in advance. The values of bits in the preamble of the GPS messageand certain other bits are indeed known in advance. But as mentioned notall data bits are known, so the ½ cycle slip can go undetected for somefinite amount of time until known data bits do arrive.

FIGS. 4A-4D shows plots of in-phase and quadrature-phase signals andalso shows plots of two carrier discriminators: one for a Costas Loopand one for a standard PLL. All signals are plotted as a function of thephase error 501, this phase error is defined asphase error=(carrier phase of received signal)−(phase of NCO).

FIG. 4A shows the in-phase component I_(p), 500, which is periodic overthe carrier's wavelength, λ. FIG. 4B shows the quadrature phasecomponent Q_(p), 510, also periodic with period λ. FIG. 4C plots thecarrier discriminator, CD=Q_(p) sign(I_(p)), for a Costas loop. The CD520 is periodic with period λ/2. Tracking can occur at any zero crossingof the CD function, such as 522, 523, and 524, all of which areseparated from one another by λ/2. Tracking-loop feedback control is inthe correct direction when the CD function 520 is positive to the rightof the zero crossing and negative to the left. Each zero crossing, forexample 523, is thus a stable track point. Track point 523 remains astable track point so long as the tracking error does not exceed thepull-in-zone 525 of width λ/2. If error exceeds the pull-in-zone 525,the NCO phase may “slip” so that a new track point is established, suchas depicted at 522 or 524. This is the phenomenon that results in the ½cycle ambiguity of a Costas loop. Similar arguments hold for otherimplementations of Costas loop discriminators, such asCD=Tan⁻¹(Q _(p) /I _(p)).

A conventional (non Costas) PLL is shown in FIG. 4D using the simplecarrier discriminator, CD=Q_(p). The CD 530 is periodic with a period ofλ. Zero crossings 532, 533, and 534 are stable track points alsoseparated by λ. A zero crossing such as 536 is not a stable track pointsince it does not meet the condition that CD is positive to the rightand negative to the left. Phase errors in the vicinity of 536 will bedriven to either 533 or 534 by the feedback control. Thus, thepull-in-zone 535 is of width λ which is twice the width of that of theCostas loop. Therefore, is becomes evident that a conventional PLL isless apt to cycle slip due to the wider pull-in-zone. Furthermore, itcannot exhibit a ½ cycle ambiguity since it tracks only to integercycles. Unfortunately, a conventional PLL only works when the carriersignal is not modulated by unknown data, as is the case with GPSbroadcast signals.

One way to achieve the benefits of a conventional PLL when employing aCostas loop is to know the sign of the modulating data in advance. It isthen possible to use the discriminatorCD=Q _(p) sign(I _(data))where I_(data) is defined as having the known sign of the modulatingdata. Since I_(data) is not a function of phase track error, the CD onlydepends on the term Q_(p) and is thus similar to a conventional PLLdiscriminator in this respect. For example, the PLL discriminator shownin FIG. 4D is dependant only on Q_(p). A Costas loop employing the abovecarrier discriminator behaves like a PLL and thus has a pull-in-zone ofwidth λ rather than a width of λ/2.

It is worth noting that even if the sign of I_(data) is inverted so thatit is opposite that of the true data, the Costas loop will simplyundergo a onetime shift in phase of ½ cycle to negate the sign mismatch,but will then exhibit properties similar to those experienced when usingthe actual sign of the data. Consequently, the following discriminatoralso enables a Costas loop to behave like a conventional PLL, albeitwith inverted data output.CD=Q _(p) sign(−I _(data))

Referring now to FIG. 5 depicting two tracking loops 600 and 650 inaccordance with an exemplary embodiment. The master tracking loop 600 isconnected to a master antenna 601 while the slave tracking loop 650 isconnected to a slave antenna 651. Both tracking loops employ a Costasloop. The carrier discriminator 604 in the master tracking loop issupplied both I_(p) and Q_(p) (602 and 603) both of which originate fromthe master tracking loop 600. The carrier discriminator output is fed tothe track filter 605 which commands the NCO 606. The master track loopis substantially the same in concept, as the track loop describedpreviously and shown as FIG. 3.

The slave track loop 650 has a subtle difference, however. Its own I_(p)data 652 is not fed to the salve carrier discriminator 654, but rather,I_(p) data 602 from the master track loop 600 is used in its place. Theslave carrier discriminator 654 still makes use of its own Q_(p) data653. As with the master, the slave track filter 655 drives the carrierNCO 656 of the slave tracking loop 650.

Mathematically, the master and slave discriminators areCD _(master) =Q _(master) sign(I _(master))CD _(slave) =Q _(slave) sign(I _(master))Where we have adopted the following notation:

-   I_(master) is the in-phase data from the master track loop;-   Q_(master) is the quadrature-phase data from the master track loop;-   I_(slave) is the in-phase data from the slave track loop; and-   Q_(slave) is the quadrature-phase data from the slave track loop.

Now consider the slave's carrier discriminatorCD _(slave) =Q _(slave) sign(I _(master))

Clearly, CD_(slave) depends only on the slave track loop through thequadrature-phase component, Q_(slave). For sign compensation, it nolonger depends on its own in-phase component, I_(slave), but instead hasan external dependence on the master's in-phase component, I_(master).As a consequence, the slave track loop 650 behaves more like aconventional PLL than a Costas loop. This is readily seen if youconsider a carrier discriminator that uses the sign of the actual dataCD _(slave) =Q _(slave) sign(I _(data)).

If I_(master) is taken as the true value of the data(I_(master)=I_(data)), then the conventional PLL behavior is evident.The master's in-phase data does indeed maintain the same sign (ormaintains consistent opposite sign) as the true data bits due to thenature of its Costas tracking loop. Furthermore, the data bits withinthe satellite broadcast signal arrive at master and slave antennas atsubstantially the same time as compared to the width of a data bit. Whenantennas are spaced apart by less than several meters (as they will bein a typical attitude determination device), the arrival time differencebetween master and slave data bits is less than ten nanoseconds, whichis insignificant compared to the 20 millisecond data bit duration. Thus,as long as I_(master) maintains a consistent sign or consistent oppositesign to the true data, the pull-in-zone for the slave is widened fromλ/2 to λ.

In practice, the master track loop 600 will sometimes slip. If it slips½ cycle (or any integer number of cycles plus ½ cycle), the slavecontrol loop 650 will react by steering its NCO phase to an offset of ½cycle to compensate for the sign reversal of I_(master). This is exactlythe behavior that is desired for an attitude determining device, since ½cycle phase offsets of the master e.g., 202, 600 and slave e.g., 203,204, 650 are kept identical by the disclosed scheme. As such, any ½cycle phase offsets will cancel in the difference between master andslave carrier phase. The carrier phase difference will only exhibitwhole integer cycle phase ambiguities. Whole cycles are much easier todeal with than ½ cycles both in terms of estimating the ambiguities andwhen detecting cycle slips that may sometimes occur. Consequently,coupling the master's in-phase data 602 to the slave's carrierdiscriminator 654 yields a significant advantage.

FIG. 6 is a simplified block diagram depicting an implementation of themethodology and apparatus of FIG. 5; however, in this instance, two ormore slave systems are depicted rather than one. In this figure, themaster track loop 700 supplies its in-phase data, denoted in the figureby reference numeral 703 to its own CD and to the CDs of slave trackingloop 701 and slave tracking loop 702. Any number of slave track loopsmay be augmented by applying the in-phase term from a single master toeach of the slave carrier discriminators. All slaves will thus maintaina ½ cycle alignment with the master. The differential carrier phasebetween master and slave or, for that matter any slave pair, will befree of ½ cycle ambiguities.

In some attitude systems it is advantageous to not only deliver thein-phase data from the master tracking loop, e.g., 700 to the slavetrack loops, e.g., 701, 702, but share other track loop data as well.For example, when the master and slave antennas undergo motion thatexhibits concurrent or similar dynamics, the tracking loops preferablyneed to react similarly and sharing of data between track loops isbeneficial. In particular, in an attitude or heading system thatexperiences high translational accelerations (such as when mounted on anaircraft) but low rotational accelerations, it is likely that thedominant translational accelerations are seen by all antennas nearlyequally. Track loops receiving data from each antenna should reactnearly identically to track the common carrier phase accelerations.

In another situation, there may be minute physical accelerationsexperienced at the antennas, as for example, when a heading device ismounted on a large ship. Even if physical accelerations are small, thereceiver's own oscillator undergoes frequency perturbations that resultin apparent carrier phase accelerations. However, the oscillator isshared between master and slave tracking modules and the oscillatorinduced accelerations will be identical across each track loop.

As a solution of the aforementioned problem, in another exemplaryembodiment, carrier phase tracking errors are summed (or averaged) andsupplied to a responsive, high-bandwidth track loop filter that isshared among track loops. A lower bandwidth filter that is independentfor each track loop, is utilized to track the slower but non-commondynamics using the individual phase errors of each system. A sharedhigh-bandwidth track loop is employed to dominate the high frequency andnoise response. As such, the noise induced into the individual carrierphase measurements will be similar and will cancel in the carrier phasedifferences that are formed as part of the attitude solution. This,advantageously, results in smoother differential carrier phaseobservations and ultimately attitude angles that are smoother as well.

FIG. 7 shows an exemplary embodiment of a multiple track loop receiversystem utilizing not only a shared in-phase component, but sharedcarrier discriminator outputs as well. A master track signal processor801 and a slave track signal processor 851 receive carrier data fromantennas 800 and 850, respectively. As per the methodology describedabove, the in-phase data 802 for the master tracking loop 801 isdelivered to both master and slave carrier discriminators 804 and 854respectively, so that ½ cycle phase tracking alignment can be realized.Master carrier discriminator 804 computes a phase error 805 and slavecarrier discriminator 854 computes a phase error 855. Each phase erroris proportional to the difference of the respective NCO generated phaseand the carrier phase of the received signal.

Uniquely in this embodiment, phase tracking errors 805 and 855 of themaster and slave, respectively, are each coupled to both track loops.Phase error 805 is fed to a summer 807 where it is added to phase error855 that has been multiplied by a scale factor α using amplifier 856.Similarly, phase error 855 is fed to a summer 857 where it is added tophase error 805 that has also been multiplied by α using amplifier 806.The value α of amplifiers 806 and 856 is identical in this embodiment,however, other values may be employed. The summed signal produced bysummer 807 is fed to the track filter 808 for the master tracking loop801, which is either a proportional plus integral filter or some othertrack filter that results in a stable feedback control. The track filter808 then delivers the NCO step 809 to the carrier NCO for the mastertracking loop 801. Similarly, the summed signal produced by summer 857is fed to the track filter 858 for the slave tracking loop 851, again,which is either a proportional plus integral filter or some other trackfilter that results in a stable feedback control. The track filter 858then delivers the NCO step 859 to the carrier NCO for the slave trackingloop 851.

FIG. 7 depicts an exemplary embodiment of information sharing trackingloops that realizes, for each track-loop, a common high-bandwidthresponse and an independent low-bandwidth response. In one exemplaryembodiment, the value of a is selected to be preferably less than one,but somewhat near to one. The closer alpha is to one, the lessindependent the track loops become. If α is exactly one, both trackloops are supplied exactly the same data and therefore generate the sameNCO command. In practice, antennas are typically in separate locationsor move separately and therefore require slightly different NCO commandsto properly track, thus values other than one are desirable. On theother hand, if the value of α for both is zero, afterward both trackloops are completely independent of one another (other than the sharedin-phase signal) and each system is similar to that depicted in FIG. 5.It is noteworthy to appreciate that setting α to zero may beadvantageous during certain instances of operation. For example, duringtracking loop initialization more independence may be desired.Conversely, in steady-state operation, choosing α as some number near toone, such as 0.9, gives a dominant common response, with a less dominantindependent response, but still assures some independence of the trackloops 801, 851. No matter what α is chosen, track loop filters 808 and858 are designed so that overall system response is stable and meetssystem bandwidth and settling requirements.

Continuing now to FIG. 8, a block diagram is depicted of yet anotherexemplary embodiment exhibiting a more flexible configuration forimplementing a common high-bandwidth response and an independentlow-bandwidth response. In the figure, a common high-bandwidth trackloop filter 922 is completely independent of two individually-steered,low-bandwidth filters 907 and 957 for the master tracking loop 900 andslave tracking loop 950, respectively. Advantageously, with thisembodiment tracking loop parameters, such as proportional plus integralgains, may be adjusted independently to give both desired low-bandwidthand desired high-bandwidth responses. It will be appreciated that up toand including the carrier discriminators 904 and 954, the track loopsare substantially identical to those shown in FIG. 7. The phase trackingerror 905 is proportional to the difference in phase between the phaseof the NCO 910 and the carrier phase arriving at antenna for the mastertracking loop 900. Similarly, phase tracking error 955 is proportionalto the difference in phase between the phase of the NCO 960 and thecarrier phase arriving at antenna for the slave tracking loop 950.

Track errors 905 and 955 are summed at 920; the sum 921 is thendelivered to the common track filter 922. The common track loop filterhas its own set of parameters, such as proportional and integral gains.The output 923 of the common track loop is fed to the master NCO throughsummer 924 and to the slave NCO through summer 925.

The master's independent track loop filter 907 utilizes only themaster's track error 905 which is scaled through the amplifier 906having a gain of β. Similarly, the slave's independent track loop filter957 utilizes only the slave's track error 955 which is scaled throughamplifier 956 of gain β. In this embodiment, both track loops 907 and957 employ identical filters (although it will be appreciated that theyneed not), which are typically adjusted to yield lower bandwidthresponse than the common track filter 922. The output 908 of themaster's independent track filter is added to the common track filteroutput 923 and fed to the master's carrier NCO 910. The output 958 ofthe slave independent track filter is added to the common track filteroutput 923 and fed to the slave 's carrier NCO 960. Ultimate track loopresponse and degree of track loop independence is readily configurableby the designer.

FIG. 7 and FIG. 8 are just two illustrative configurations for realizingcarrier track loops that have a common mode noise-induced phase errorand common ½ cycle ambiguity, these commonalities canceling whendifferencing the phase from each NCO. One skilled in the art may readilyenvision numerous variations and other realizations that would lead toand achieve similar results. Moreover, although this disclosure thus farhas made reference to the application of this invention with respect toan illustration as an attitude or heading system, it may readily beapplied to a more general class of GNSS devices and applications. Onesuch application would be a local survey system where one antenna isused as a reference and another is used to survey a location relative toa reference. Both antennas of which are connected to a common receiverthat maintains tracking of signals arriving at each antenna.

To be consistent with the disclosure herein, the two systems need onlyensure that the tracking loops of two or more receivers can share dataat a rate consistent with the track loops update rate and that antennasthat receive the carrier signals be sufficiently close together so thatdata bit transitions occur at roughly the same time (e.g., within 10%)relative to the in-phase and quadrature phase accumulation windowstart/stop times. It will be further appreciated that these constraintsmay be relaxed if the master and slave tracking loops run in non-realtime (perhaps in post processing software) where methods can be appliedto share and align data without concern for real-time processingconstraints.

Furthermore, pipeline delays can be introduced into a real-time system'sdata flow so that even when antennas are spaced widely (or signalsarrive at different times for other reasons such as hardware orfiltering delays), data bit transitions can be aligned between trackloops. In many circumstances, different bit arrival times are not anissue, for even if data accumulations occur over windows as small as onemillisecond, antenna spacing would have to exceed 30 kilometers beforesignal travel delays induced a 10% misalignment of the accumulationwindows.

It will be evident that there exist numerous numerical methodologies inthe art for implementation of mathematical functions, in particular asreferenced here, including, but not limited to, linearizations, leastsquares approximations, filters, Kalman filters, taking maximums, andsummations. While many possible implementations exist, a particularmethod of implementation as employed to illustrate the exemplaryembodiments should not be considered limiting.

The system and methodology described in the numerous embodimentshereinbefore provide a system and method of positioning or attitudedetermination that is effective and advantageously exploits GlobalNavigation Satellite System (GNSS) signals to infer differential pathlength of carrier signals arriving at two or more antennas. Inparticular, the described embodiments provide an improved tracking loopfor carrier phase tracking. In addition, the disclosed invention may beembodied in the form of computer-implemented processes and apparatusesfor practicing those processes. The present invention can also beembodied in the form of computer program code containing instructionsembodied in tangible media, such as floppy diskettes, CD-ROMs, harddrives, or any other computer-readable storage medium, wherein when thecomputer program code is loaded into and executed by a computer, thecomputer becomes an apparatus for practicing the invention. The presentinvention can also be embodied in the form of computer program code, forexample, whether stored in a storage medium, loaded into and/or executedby a computer, or as data signal transmitted, whether a modulatedcarrier wave or not, over some transmission medium, such as overelectrical wiring or cabling, through fiber optics, or viaelectromagnetic radiation, wherein, when the computer program code isloaded into and executed by a computer, the computer becomes anapparatus for practicing the invention. When implemented on ageneral-purpose microprocessor, the computer program code segmentsconfigure the microprocessor to create specific logic circuits.

It will be appreciated that the use of “first” and “second” or othersimilar nomenclature for denoting similar items is not intended tospecify or imply any particular order unless otherwise specificallystated. Likewise the use of “a” or “an” or other similar nomenclature isintended to mean “one or more”, unless otherwise specifically stated.

While the invention has been described with reference to an exemplaryembodiment thereof, it will be understood by those skilled in the artthat the present disclosure is not limited to such exemplary embodimentsand that various changes may be made and equivalents may be substitutedfor elements thereof without departing from the scope of the invention.In addition, a variety of modifications, enhancements, and/or variationsmay be made to adapt a particular situation or material to the teachingsof the invention without departing from the essential spirit or scopethereof Therefore, it is intended that the invention not be limited tothe particular embodiment disclosed as the best mode contemplated forcarrying out this invention, but that the invention will include allembodiments falling within the scope of the appended claims.

1. A method of reducing Global Navigation Satellite System (GNSS)carrier tracking loop ambiguities comprising: receiving a plurality ofGNSS satellite signals with a first antenna in operable communicationwith a first tracking device and a second antenna in communication witha second tracking device in at least one GNSS receiver; and sharing ofdata between said first tracking device and said second tracking device,said sharing configured to facilitate a commonality in a carrier phasederived in said first tracking device and said second.tracking device;said sharing resulting in a cancellation in said commonality when adifference phase is formed between a carrier phase from said firsttracking device and another carrier phase from said second trackingdevice.
 2. The method of claim 1 wherein said difference phase issingle- or double-difference phases corresponding to one or more GNSSsatellites for said first tracking device and said second trackingdevice.
 3. The method of claim 2 further including determining at leastone of an integer ambiguity value, a position corresponding to saidfirst antenna, or a position corresponding to said second antenna. 4.The method of claim 2 further including determining at least oneattitude angle for at least said first antenna and said second antenna.5. The method of claim 1 wherein said data includes at least one ofin-phase data or quadrature-phase data.
 6. The method of claim 1 whereinsaid commonality includes at least one of common mode phase error andcommon ½ cycle ambiguity for said carrier phase derived in each of saidfirst tracking device and said second tracking device.
 7. The method ofclaim 1 wherein at least one of said first tracking device or saidsecond tracking device employs a Costas loop.
 8. The method of claim 7further including ensuring that any cycle slip that arises on a carriersignal tracked from one said first antenna or first tracking device iscompensated for the carrier signal tracked for said second antenna orsecond tracking device.
 9. A storage medium encoded with amachine-readable computer program code for reducing Global NavigationSatellite System (GNSS) carrier tracking loop ambiguities, said storagemedium including instructions for causing a computing system toimplement the method of claim
 1. 10. A computer data signal for reducingGlobal Navigation Satellite System (GNSS) carrier tracking loopambiguities, the computer data signal comprising code configured tocause a processor to implement the method of claim
 1. 11. A system forreducing Global Navigation Satellite System (GNSS) carrier tracking loopambiguities comprising: a first antenna in operable communication with afirst tracking device configured to receive a plurality of GNSSsatellite signals; a second antenna in communication with a secondtracking device configured to receive a plurality of GNSS satellitesignals; said first tracking device and said second tracking device inat least one GNSS receiver; and wherein said first tracking device andsaid second tracking device are configured to share data therebetween tofacilitate a commonality in a carrier phase derived in said firsttracking device and said second tracking device and resulting in acancellation in said commonality when a difference phase is formedbetween a carrier phase from said first tracking device and anothercarrier phase from said second tracking device.
 12. The system of claim11 wherein said difference phase is single- or double-difference phasescorresponding to one or more GNSS satellites for said first trackingdevice and said second tracking device.
 13. The system of claim 12wherein at least one of said first tracking device or said secondtracking device is configured to facilitate determining at least one ofan integer ambiguity value, a position corresponding to said firstantenna, or a position corresponding to said second antenna.
 14. Thesystem of claim 12 wherein at least one of said first tracking device orsaid second tracking device is configured to facilitate determining atleast one attitude angle based on known geometry constraints for atleast said first antenna and said second antenna.
 15. The system ofclaim 11 wherein said data includes at least one of in-phase data orquadrature-phase data.
 16. The system of claim 11 wherein saidcommonality includes at least one of common mode phase error and common½ cycle ambiguity for said carrier phase derived in each of said firsttracking device and said second tracking device.
 17. The system of claim11 wherein said first tracking device and said second tracking deviceare established as a master tracking device and slave tracking devicerespectively in that said slave tracking device receives said data fromsaid master tracking device.
 18. The system of claim 11 wherein at leastone of said first tracking device or said second tracking device employsa Costas loop.
 19. A system for reducing Global Navigation SatelliteSystem (GNSS) carrier tracking loop ambiguities comprising: means forreceiving a plurality of GNSS satellite signals with a first antenna inoperable communication with a first tracking device and a second antennain communication with a second tracking device in at least one GNSSreceiver; and means for sharing of data between said first trackingdevice and said second tracking device, said sharing configured tofacilitate a commonality in a carrier phase derived in said firsttracking device and said second tracking device; said sharing resultingin a cancellation in said commonality when a difference phase is formedbetween a carrier phase from said first tracking device and anothercarrier phase from said second tracking device.
 20. A method of reducinghalf cycle ambiguities or cycle slips in GNSS differential carrier phasedeterminations comprising: designating a first tracking device as amaster tracking device; designating a second tracking device as a slavetracking device; sharing information between Costas tracking loops ofsaid master tracking device and said slave tracking device; said slavetracking device driven by a carrier discriminator employing in-phasedata from said master tracking device in place of internally generatedin-phase data.